To produce laser-driven x-ray beams, the process of inverse Compton (or Thomson) scattering of a laser pulse with a laser-accelerated electron pulse (driven by the same laser system) is used. The challenge is to overlap—in both time and space—the scattering laser beam (pulse) with the electron beam (pulse), both of which have spot-sizes that are on the micron-scale, and then to maintain their overlap reproducibly despite their tendency to drift apart. The other challenge is to measure the x-ray signal despite the large background noise produced by bremsstrahlung radiation when the high energy electron beams from the wakefield accelerator interact with solid matter (in either the electron beam dump or other objects used in the device) located in close proximity to the detector.